Dander is an animal's tiny flakes of skin. People who are allergic to cats are typically sensitive to their dander.
Furry animals shed both hair and microscopic dander — and it's more common to be allergic to the dander. If you have dog allergies, your body overreacts to breathing in the dander of your best friend's chihuahua, making you sneeze. Another kind of dander is an angry or frustrated feeling, which shows up in the phrase "get your dander up." You might say, "My dander was up from the minute he made that offensive joke."